1. Field of the Invention
The invention relates to continuous-time filtering. More particularly, it relates to filtering in a feedback control loop, for example in a sigma-delta (ΣΔ) modulator. Analog ΣΔ modulators can be used, for example, in radar receivers or telecommunications systems, in particular to improve the resolution of analog-digital encoding.
2. Description of the Prior Art
The ΣΔ modulation of a signal consists of the encoding of this signal on a small number of bits but with a far higher resolution than the theoretical limit given by the number of bits. To this end, a feedback control loop is made. The quantization device, which limits the resolution, is placed at output of this loop as can be seen in the generic diagram of FIG. 1(a).
If the signal is a digital signal, the ΣΔ modulator unit is made as a digital device. When the digital signal at the input of the ΣΔ modulator comprises N bits, the return signal comprises N bits including N−n null least significant bits (LSB), the input signal of the integration device 1 comprises N+1 bits, and the signal at the input and output of the quantization device 2 respectively comprises N bits and n bits (where n is far smaller than N). Thus, the signal encoded at output of the ΣΔ modulator has a small number of bits and high resolution in the band. This is typically the case in CD readers where the output of the modulator is obtained on 1 bit whereas the input signal is encoded on about 20 bits.
However, if the signal is an analog signal, with the analog-digital converter 2 (a source of quantization that limits the resolution) being placed at output of the loop as can be seen in FIG. 1(b), the result is that the filtering 11, which integrates the input/output error, is necessarily an analog filtering. Two cases arise. The first is that frequency of the signal is low enough. In this case the signal may be sampled at the entry to the loop (not shown) before the filtering 11, which is then done in the discrete time domain (using switched capacitors for example). The second possible case arises at higher frequencies, especially on carriers: in this case the discrete time techniques (switched-capacitor or switched-current loop techniques, especially) are inappropriate. The filtering 11 can then be continuous-time filtering. The most commonly used technology here is the GmC technology (entailing the use of transconductance amplifiers). The sampling is then done at output of the loop, just before the quantization (analog-digital conversion).
Furthermore, referring again to the high frequencies, the cumulated conversion times of the analog-digital converter (ADC) 2 and of the digital-analog analog converter de (DAC) 3 are spread over several sampling periods instead of being smaller than a single period. This problem disappears if the encoding is done on only one bit, but then the very high non-linearity of the encoding function means that it is not possible to define a criterion of stability for the ΣΔ modulator with certainty. A multi-bit encoding is then preferred. For this encoding, the response of the open loop may be considered to be a first-order linear response.
The making of the loop filter 11 must then resolve the classic problem of feedback control loops: providing the maximum gain (and thus minimizing the error between the feedback-controlled signal and the control) while preserving the stability of the loop. This is especially difficult to achieve since the total delay time of the loop, also known as the latency number, is great. It is the difficulty of finding filtering functions that perform well, even in the presence of high latency numbers, that has hitherto hampered the development of continuous-time ΣΔ modulators.